Support Custom Connectives

parse_magic.py

@@ -4,6 +4,7 @@ Parses the Magic Ugly Data File Format
 Assumes the base logic is R with no extra connectives
 """
 import argparse
+import re
 import sys
 from typing import TextIO, List, Optional, Tuple, Set, Dict
 
@@ -13,7 +14,8 @@ from logic import (
     Conjunction,
     Negation,
     Necessitation,
-    Disjunction
+    Disjunction,
+    Operation
 )
 from vsp import has_vsp
 
@@ -21,161 +23,320 @@ class SourceFile:
     def __init__(self, fileobj: TextIO):
         self.fileobj = fileobj
         self.current_line = 0
+        self.reststr = ""
 
-    def __next__(self):
-        contents = next(self.fileobj)
+    def next_line(self):
+        """
+        Grabs the next line.
+        If reststr is populated return that, otherwise
+        consume generator
+        """
+        if self.reststr != "":
+            reststr = self.reststr
+            self.reststr = ""
+            return reststr
+
+        contents = next(self.fileobj).strip()
         self.current_line += 1
         return contents
 
+    def __next__(self):
+        """
+        Grabs the next word token from the stream
+        """
+        if self.reststr == "":
+            self.reststr = next(self.fileobj).strip()
+            self.current_line += 1
+
+        tokens = self.reststr.split(" ")
+        next_token = tokens[0]
+        self.reststr = " ".join(tokens[1:])
+
+        return next_token
+
 class UglyHeader:
-    def __init__(self, negation: bool, necessitation: bool):
+    def __init__(self, negation: bool, necessitation: bool, custom_model_functions: List[Tuple[int, str]]):
+        # Booleans describing the logical fragment
         self.negation = negation
         self.necessitation = necessitation
+        # List of custom model functions described as
+        # a sequence of (adicity, symbol) pairs
+        self.custom_model_functions = custom_model_functions
 
 class ModelBuilder:
     def __init__(self):
         self.size : int = 0
         self.carrier_set : Set[ModelValue] = set()
-        self.num_negation: int = 0
         self.mnegation: Optional[ModelFunction] = None
-        self.num_order: int = 0
         self.mconjunction: Optional[ModelFunction] = None
         self.mdisjunction: Optional[ModelFunction] = None
-        self.num_designated: int = 0
         self.designated_values: Set[ModelValue] = set()
-        self.num_implication: int = 0
         self.mimplication: Optional[ModelFunction] = None
-        self.num_necessitation: int = 0
         self.mnecessitation: Optional[ModelFunction] = None
+        # Map symbol to model function
+        self.custom_model_functions: Dict[str,  ModelFunction] = {}
+
+class Stage:
+    def __init__(self, name: str):
+        self.name = name
+        self.next: Optional['Stage'] = None
+        self.previous: Optional['Stage'] = None
+        # This corresponds to a portion of the model name in MaGIC
+        self.num = 0
+
+    def increment(self):
+        self.num += 1
+
+    def reset(self):
+        self.num = 0
+
+    def __str__(self):
+        return self.name
+
+class Stages:
+    def __init__(self):
+        end_stage = Stage("end")
+        self.stages: Dict[str, Stage] = {"end": end_stage}
+        self.last_added_stage: Stage = end_stage
+        self.first_stage: Optional[Stage] = None
+
+    def add(self, name: str):
+        stage = Stage(name)
+        stage.next = stage
+
+        stage.previous = self.last_added_stage
+
+        # End stage is a sink so don't
+        # mark any stages as next
+        if self.last_added_stage.name != "end":
+            self.last_added_stage.next = stage
+        else:
+            # If this is triggered, than this is the first
+            # stage added
+            self.first_stage = stage
+
+        self.stages[name] = stage
+        self.last_added_stage = stage
+
+    def reset_after(self, name):
+        """
+        Resets the stage counters after a given stage.
+        This is to accurately reflect the name of the
+        model within MaGIC.
+        """
+        stage = self.stages[name]
+        while stage.name != "process_model":
+            stage.reset()
+            stage = stage.next
+
+    def get(self, name):
+        return self.stages[name]
+
+    def name(self):
+        result = ""
+        stage = self.first_stage
+        if stage is None:
+            return ""
+
+        result = f"{stage.num}"
+        if stage.next == "process_model":
+            return result
+
+        stage = stage.next
+        while stage is not None:
+            result += f".{stage.num}"
+            if stage.next.name != "process_model":
+                stage = stage.next
+            else:
+                stage = None
+
+        return result
+
+
+def derive_stages(header: UglyHeader) -> Stages:
+    stages = Stages()
+    stages.add("size")
+    if header.negation:
+        stages.add("negation")
+    stages.add("order")
+    stages.add("designated")
+    stages.add("implication")
+    if header.necessitation:
+        stages.add("necessitation")
+    for (adicity, symbol) in header.custom_model_functions:
+        stages.add(f"custom--{adicity}--{symbol}")
+    stages.add("process_model")
+
+    # After processing the model, go to the previous stage
+    stages.get("process_model").next = stages.get("process_model").previous
+
+    return stages
 
 def parse_matrices(infile: SourceFile) -> List[Tuple[Model, Dict]]:
-    solutions = [] # Reset
+    solutions = []
     header = parse_header(infile)
+    stages = derive_stages(header)
+    first_run = True
     current_model_parts = ModelBuilder()
-    process_sizes(infile, header, current_model_parts, solutions)
+    stage = stages.first_stage
+    while True:
+        match stage.name:
+            case "end":
+                break
+            case "process_model":
+                process_model(stages.name(), current_model_parts, solutions)
+                stage = stage.next
+            case "size":
+                processed = process_sizes(infile, current_model_parts, first_run)
+                first_run = False
+                if processed:
+                    stage.num = current_model_parts.size + 1
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
+            case "negation":
+                processed = process_negations(infile, current_model_parts)
+                if processed:
+                    stage.increment()
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
+            case "order":
+                processed = process_orders(infile, current_model_parts)
+                if processed:
+                    stage.increment()
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
+            case "designated":
+                processed = process_designateds(infile, current_model_parts)
+                if processed:
+                    stage.increment()
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
+            case "implication":
+                processed = process_implications(infile, current_model_parts)
+                if processed:
+                    stage.increment()
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
+            case "necessitation":
+                processed = process_necessitations(infile, current_model_parts)
+                if processed:
+                    stage.increment()
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
+            case _:
+                custom_stage = re.search(r"custom--(\d+)--(\S+)", stage.name)
+                if custom_stage is None or len(custom_stage.groups()) != 2:
+                    raise NotImplementedError(f"Unrecognized Stage: {stage.name}")
+                adicity, symbol = custom_stage.groups()
+                adicity = int(adicity)
+                processed = process_custom_connective(infile, symbol, adicity, current_model_parts)
+
+                if processed:
+                    stage.increment()
+                    stage = stage.next
+                else:
+                    stages.reset_after(stage.name)
+                    stage = stage.previous
+
     return solutions
 
-def process_sizes(infile: SourceFile, header: UglyHeader, current_model_parts: ModelBuilder, solutions: List[Tuple[Model, Dict]]):
-    """Stage 1"""
+def process_sizes(infile: SourceFile, current_model_parts: ModelBuilder, first_run: bool) -> bool:
+    try:
+        size = parse_size(infile, first_run)
+    except StopIteration:
+        return False
+    if size is None:
+        return False
 
-    first_run = True
+    carrier_set = carrier_set_from_size(size)
+    current_model_parts.carrier_set = carrier_set
+    current_model_parts.size = size
 
-    while True:
-        print("Processing next size")
-        try:
-            size = parse_size(infile, first_run)
-            first_run = False
-        except StopIteration:
-            # For some reason, when necessitation is enabled this doesn't
-            # have a -1 on the last line
-            break
-        if size is None:
-            break
+    return True
 
-        carrier_set = carrier_set_from_size(size)
-        current_model_parts.size = size
-        current_model_parts.carrier_set = carrier_set
-        process_negations(infile, header, current_model_parts, solutions)
-
-def process_negations(infile: SourceFile, header: UglyHeader, current_model_parts: ModelBuilder, solutions: List[Tuple[Model, Dict]]):
+def process_negations(infile: SourceFile, current_model_parts: ModelBuilder) -> bool:
     """Stage 2 (Optional)"""
-    num_negation = 0
-    while True:
-        print("Processing next negation")
-        mnegation = None
-        if header.negation:
-            mnegation = parse_single_negation(infile, current_model_parts.size)
-            if mnegation is None:
-                break
-            num_negation += 1
+    mnegation = parse_single_monadic_connective(infile, "¬", current_model_parts.size)
+    if mnegation is None:
+        return False
 
-        current_model_parts.num_negation = num_negation
-        current_model_parts.mnegation = mnegation
+    current_model_parts.mnegation = mnegation
+    return True
 
-        process_orders(infile, header, current_model_parts, solutions)
-
-        if not header.negation:
-            break
-
-def process_orders(infile: SourceFile, header: UglyHeader, current_model_parts: ModelBuilder, solutions: List[Tuple[Model, Dict]]):
+def process_orders(infile: SourceFile, current_model_parts: ModelBuilder) -> bool:
     """Stage 3"""
-    num_order = 0
-    while True:
-        print("Processing next order")
-        result = parse_single_order(infile, current_model_parts.size)
-        if result is None:
-            break
-        num_order += 1
-        mconjunction, mdisjunction = result
-        current_model_parts.num_order = num_order
-        current_model_parts.mconjunction = mconjunction
-        current_model_parts.mdisjunction = mdisjunction
-        process_designateds(infile, header, current_model_parts, solutions)
+    result = parse_single_order(infile, current_model_parts.size)
+    if result is None:
+        return False
 
-def process_designateds(infile: SourceFile, header: UglyHeader, current_model_parts: ModelBuilder, solutions: List[Tuple[Model, Dict]]):
+    mconjunction, mdisjunction = result
+    current_model_parts.mconjunction = mconjunction
+    current_model_parts.mdisjunction = mdisjunction
+
+    return True
+
+def process_designateds(infile: SourceFile, current_model_parts: ModelBuilder) -> bool:
     """Stage 4"""
-    num_designated = 0
-    while True:
-        print("Processing next designated")
-        designated_values = parse_single_designated(infile, current_model_parts.size)
-        if designated_values is None:
-            break
-        num_designated += 1
-        current_model_parts.num_designated = num_designated
-        current_model_parts.designated_values = designated_values
-        process_implications(infile, header, current_model_parts, solutions)
+    designated_values = parse_single_designated(infile, current_model_parts.size)
+    if designated_values is None:
+        return False
 
-def process_implications(
-    infile: SourceFile, header: UglyHeader, current_model_parts: ModelBuilder, solutions: List[Tuple[Model, Dict]]):
+    current_model_parts.designated_values = designated_values
+    return True
+
+def process_implications(infile: SourceFile, current_model_parts: ModelBuilder) -> bool:
     """Stage 5"""
-    if header.necessitation:
-        num_implication = 0
-        while True:
-            print("Processing next implication")
-            instr = next(infile).strip()
-            mimplication, reststr = parse_single_implication(instr, infile.current_line, current_model_parts.size)
-            if mimplication is None:
-                break
-            num_implication += 1
-            current_model_parts.num_implication = num_implication
-            current_model_parts.mimplication = mimplication
-            process_necessitations(infile, reststr, header, current_model_parts, solutions)
-    else:
-        results = parse_implications(infile, current_model_parts.size)
-        for num_implication, mimplication in enumerate(results, 1):
-            current_model_parts.num_implication = num_implication
-            current_model_parts.mimplication = mimplication
-            process_model(current_model_parts, solutions)
+    mimplication = parse_single_dyadic_connective(infile, "→", current_model_parts.size)
+    if mimplication is None:
+        return False
 
-def process_necessitations(infile: SourceFile, instr: str, header: UglyHeader, current_model_parts: ModelBuilder, solutions: List[Tuple[Model, Dict]]):
+    current_model_parts.mimplication = mimplication
+    return True
 
-    # NOTE: For some reason, one necessitation table will be on the same line as the implication table
-    mnecessitation = parse_single_necessitation_from_str(instr, infile.current_line, current_model_parts.size)
-    assert mnecessitation is not None, f"Expected Necessitation Table at line {infile.current_line}"
-    num_necessitation = 1
+def process_necessitations(infile: SourceFile, current_model_parts: ModelBuilder) -> bool:
+    mnecessitation = parse_single_monadic_connective(infile, "!", current_model_parts.size)
+    if mnecessitation is None:
+        return False
 
-    current_model_parts.num_necessitation = num_necessitation
     current_model_parts.mnecessitation = mnecessitation
-    process_model(current_model_parts, solutions)
+    return True
 
-    while True:
-        print("Processing next necessitation")
-        mnecessitation = parse_single_necessitation(infile, current_model_parts.size)
-        if mnecessitation is None:
-            break
-        num_necessitation += 1
+def process_custom_connective(infile: SourceFile, symbol: str, adicity: int, current_model_parts: ModelBuilder) -> bool:
+    if adicity == 0:
+        mfunction = parse_single_nullary_connective(infile, symbol)
+    elif adicity == 1:
+        mfunction = parse_single_monadic_connective(infile, symbol, current_model_parts.size)
+    elif adicity == 2:
+        mfunction = parse_single_dyadic_connective(infile, symbol, current_model_parts.size)
+    else:
+        raise NotImplementedError("Unable to process connectives of adicity greater than 2")
 
-        current_model_parts.num_necessitation = num_necessitation
-        current_model_parts.mnecessitation = mnecessitation
-        process_model(current_model_parts, solutions)
+    if mfunction is None:
+        return False
 
-def process_model(mp: ModelBuilder, solutions: List[Tuple[Model, Dict]]):
+    current_model_parts.custom_model_functions[symbol] = mfunction
+    return True
+
+def process_model(model_name: str, mp: ModelBuilder,  solutions: List[Tuple[Model, Dict]]):
     """Create Model"""
+    assert mp.size > 0
+    assert mp.size + 1 == len(mp.carrier_set)
+    assert len(mp.designated_values) <= len(mp.carrier_set)
     assert mp.mimplication is not None
-    assert len(mp.carrier_set) > 0
 
     logical_operations = { mp.mimplication }
-    model_name = f"{mp.size}{'.' + str(mp.num_negation) if mp.num_negation != 0 else ''}.{mp.num_order}.{mp.num_designated}.{mp.num_implication}{'.' + str(mp.num_necessitation) if mp.num_necessitation != 0 else ''}"
     model = Model(mp.carrier_set, logical_operations, mp.designated_values, name=model_name)
     interpretation = {
         Implication: mp.mimplication
@@ -193,23 +354,34 @@ def process_model(mp: ModelBuilder, solutions: List[Tuple[Model, Dict]]):
         logical_operations.add(mp.mnecessitation)
         interpretation[Necessitation] = mp.mnecessitation
 
+    for custom_mf in mp.custom_model_functions.values():
+        if custom_mf is not None:
+            logical_operations.add(custom_mf)
+            op = Operation(custom_mf.operation_name, custom_mf.arity)
+            interpretation[op] = custom_mf
+
     solutions.append((model, interpretation))
-    print(f"Parsed Matrix {model.name}")
 
 def parse_header(infile: SourceFile) -> UglyHeader:
     """
     Parse the header line from the ugly data format.
-    NOTE: Currently Incomplete.
     """
-    header_line = next(infile).strip()
+    header_line = infile.next_line()
     header_tokens = header_line.split(" ")
     assert header_tokens[0] in ["0", "1"]
     assert header_tokens[6] in ["0", "1"]
+    assert len(header_tokens) >= 7
     negation_defined = bool(int(header_tokens[0]))
     necessitation_defined = bool(int(header_tokens[6]))
-    return UglyHeader(negation_defined, necessitation_defined)
+    num_custom_connectives = int(header_tokens[7])
+    custom_model_functions: List[Tuple[int, str]] = []
+    for i in range(num_custom_connectives):
+        arity = int(header_tokens[7 + (2 * i) + 1])
+        symbol = header_tokens[7 + (2 * i) + 2]
+        custom_model_functions.append((arity, symbol))
+    return UglyHeader(negation_defined, necessitation_defined, custom_model_functions)
 
-def carrier_set_from_size(size: int):
+def carrier_set_from_size(size: int) -> Set[ModelValue]:
     """
     Construct a carrier set of model values
     based on the desired size.
@@ -222,37 +394,21 @@ def parse_size(infile: SourceFile, first_run: bool) -> Optional[int]:
     """
     Parse the line representing the matrix size.
     """
-    size = int(next(infile))
-    # HACK: The first size line may be -1 due to a bug. Skip it
-    if size == -1 and first_run:
-        size = int(next(infile))
+
+    size = int(infile.next_line())
+
+    # HACK: When necessitation and custom connectives are enabled
+    # MaGIC may produce -1s at the beginning of the file
+    if first_run:
+        while size == -1:
+            size = int(infile.next_line())
 
     if size == -1:
         return None
     assert size > 0, f"Unexpected size at line {infile.current_line}"
     return size
 
-def parse_single_negation(infile: SourceFile, size: int) -> Optional[ModelFunction]:
-    """
-    Parse the line representing the negation table.
-    """
-    line = next(infile).strip()
-    if line == '-1':
-        return None
-
-    row = line.split(" ")
-    assert len(row) == size + 1, f"Negation table doesn't match size at line {infile.current_line}"
-    mapping = {}
-
-    for i, j in zip(range(size + 1), row):
-        x = mvalue_from_index(i)
-        y = parse_mvalue(j)
-        mapping[(x, )] = y
-
-    return ModelFunction(1, mapping, "¬")
-
-
-def mvalue_from_index(i: int):
+def mvalue_from_index(i: int) -> ModelValue:
     """
     Given an index, return the
     representation of the model value.
@@ -317,7 +473,7 @@ def parse_single_order(infile: SourceFile, size: int) -> Optional[Tuple[ModelFun
     """
     Parse the line representing the ordering table
     """
-    line = next(infile).strip()
+    line = infile.next_line()
     if line == '-1':
         return None
 
@@ -338,7 +494,6 @@ def parse_single_order(infile: SourceFile, size: int) -> Optional[Tuple[ModelFun
     cmapping = {}
     dmapping = {}
 
-
     for i in range(size + 1):
         x = mvalue_from_index(i)
         for j in range(size + 1):
@@ -368,7 +523,7 @@ def parse_single_designated(infile: SourceFile, size: int) -> Optional[Set[Model
     """
     Parse the line representing which model values are designated.
     """
-    line = next(infile).strip()
+    line = infile.next_line()
     if line == '-1':
         return None
 
@@ -385,17 +540,46 @@ def parse_single_designated(infile: SourceFile, size: int) -> Optional[Set[Model
     return designated_values
 
 
-def parse_single_implication(instr: str, line: int, size: int) -> Tuple[ModelFunction, str]:
-    """
-    Take the current string, parse an implication table from it,
-    and return along with it the remainder of the string
-    """
-    if instr == "-1":
-        return None, ""
+def parse_single_nullary_connective(infile: SourceFile, symbol: str) -> Optional[ModelFunction]:
+    line = infile.next_line()
+    if line == "-1":
+        return None
 
-    table = instr.split(" ")
+    row = line.split(" ")
+    assert len(row) == 1, f"More than one assignment for a nullary connective was provided at line {infile.current_line}"
 
-    assert len(table) >= (size + 1)**2, f"Implication table does not match expected size at line {line}"
+    mapping = {}
+    mapping[()] = parse_mvalue(row[0])
+    return ModelFunction(0, mapping, symbol)
+
+def parse_single_monadic_connective(infile: SourceFile, symbol: str, size: int) -> Optional[ModelFunction]:
+    line = infile.next_line()
+    if line == '-1':
+        return None
+
+    row = line.split(" ")
+    assert len(row) == size + 1, f"{symbol} table doesn't match size at line {infile.current_line}"
+    mapping = {}
+
+    for i, j in zip(range(size + 1), row):
+        x = mvalue_from_index(i)
+        y = parse_mvalue(j)
+        mapping[(x, )] = y
+
+    return ModelFunction(1, mapping, symbol)
+
+def parse_single_dyadic_connective(infile: SourceFile, symbol: str, size: int) -> Optional[ModelFunction]:
+    first_token = next(infile)
+    if first_token == "-1":
+        return None
+
+    table = []
+    try:
+        table = [first_token] + [next(infile) for _ in range((size + 1)**2 - 1)]
+    except StopIteration:
+        pass
+
+    assert len(table) == (size + 1)**2, f"{symbol} table does not match expected size at line {infile.current_line}"
 
     mapping = {}
     table_i = 0
@@ -409,65 +593,7 @@ def parse_single_implication(instr: str, line: int, size: int) -> Tuple[ModelFun
 
             mapping[(x, y)] = r
 
-    mimplication = ModelFunction(2, mapping, "→")
-    reststr = " ".join(table[(size + 1)**2:])
-    return mimplication, reststr
-
-
-def parse_implications(infile: SourceFile, size: int) -> List[ModelFunction]:
-    """
-    Parse the line representing the list of implication
-    tables.
-    """
-    line = next(infile).strip()
-
-    # Split and remove the last '-1' character
-    table = line.split(" ")[:-1]
-
-    assert len(table) % (size + 1)**2 == 0, f"Implication table does not match expected size at line {infile.current_line}"
-
-    table_i = 0
-    mimplications: List[ModelFunction] = []
-
-    for _ in range(len(table) // (size + 1)**2):
-        mapping = {}
-
-        for i in range(size + 1):
-            x = mvalue_from_index(i)
-            for j in range(size + 1):
-                y = mvalue_from_index(j)
-
-                r = parse_mvalue(table[table_i])
-                table_i += 1
-
-                mapping[(x, y)] = r
-
-        mimplication = ModelFunction(2, mapping, "→")
-        mimplications.append(mimplication)
-
-    return mimplications
-
-def parse_single_necessitation_from_str(instr: str, line: int, size: int) -> Optional[ModelFunction]:
-    """
-    Parse the line representing the necessitation table.
-    """
-    if instr == "-1":
-        return None
-
-    row = instr.split(" ")
-    assert len(row) == size + 1, f"Necessitation table doesn't match size at line {line}"
-    mapping = {}
-
-    for i, j in zip(range(size + 1), row):
-        x = mvalue_from_index(i)
-        y = parse_mvalue(j)
-        mapping[(x, )] = y
-
-    return ModelFunction(1, mapping, "!")
-
-def parse_single_necessitation(infile: SourceFile, size: int) -> Optional[ModelFunction]:
-    line = next(infile).strip()
-    return parse_single_necessitation_from_str(line, infile.current_line, size)
+    return ModelFunction(2, mapping, symbol)
 
 
 if __name__ == "__main__":